On the quasivariety of BCK-algebras and its subvarieties

DOI10.1007/BF01190766zbMath0818.06015MaRDI QIDQ1344842

James G. Raftery, Willem J. Blok

Publication date: 22 February 1995

Published in: Algebra Universalis (Search for Journal in Brave)

zbMATH Keywords

toleranceBCK-algebrasvarietyquasivarietycongruence

Mathematics Subject Classification ID

Lattices of varieties (08B15) BCK-algebras, BCI-algebras (06F35) Quasivarieties (08C15)

Related Items (18)

Varieties of commutative residuated integral pomonoids and their residuation subreducts ⋮ Factor congruences in BCK-algebras ⋮ Bounded BCK-algebras of fractions and maximal BCK-algebra of quotients ⋮ Decomposability of free Łukasiewicz implication algebras ⋮ On the variety generated by bounded pseudo-BCK-algebras ⋮ Joins and subdirect products of varieties ⋮ In memory of Willem Johannes Blok 1947-2003 ⋮ On varieties of biresiduation algebras ⋮ ASSERTIONALLY EQUIVALENT QUASIVARIETIES ⋮ Constructive logic with strong negation is a substructural logic. I ⋮ Boolean representation of bounded BCK-algebras ⋮ Free Łukasiewicz implication algebras ⋮ Unnamed Item ⋮ Lattice BCK logics with Modus Ponens as unique rule ⋮ Semisimplicity and the discriminator in bounded BCK-algebras ⋮ On the degrees of permutability of subregular varieties ⋮ Splittings in subreducts of hoops ⋮ On relative principal congruences in term quasivarieties

Cites Work

• Every BCK-algebra is a set of residuables in an integral pomonoid
• Congruence permutable and congruence 3-permutable locally finite varieties
• Ideal determined varieties need not be congruence 3-permutable
• Implication algebras are 3-permutable and 3-distributive
• Tolerance numbers, congruence $n$-permutability and BCK-algebras
• Logics without the contraction rule
• NONE OF THE VARIETY En, n>2, IS LOCALLY FINITE
• Tolerances in congruence permutable algebras
• Varieties generated by finite BCK-algebras
• An algebra related with a propositional calculus
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